{"paper":{"title":"Stability of closed characteristics on compact convex hypersurfaces in R^{2n}","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.DS","authors_text":"Xijun Hu, Yuwei Ou","submitted_at":"2014-05-16T03:26:22Z","abstract_excerpt":"Let $\\Sigma\\subset \\R^{2n}$ with $n\\geq2$ be any $C^2$ compact convex hypersurface and only has finitely geometrically distinct closed characteristics. Based on Y.Long and C.Zhu 's index jump methods \\cite{LoZ1}, we prove that there are at least two geometrically distinct elliptic closed characteristics, and moreover, there exist at least $\\varrho_{n} (\\Sigma)$ ($\\varrho_{n}(\\Sigma)\\geq[\\frac{n}{2}]+1$) geometrically distinct closed characteristics such that for any two elements among them, the ratio of their mean indices is irrational number."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.4057","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}